function E = maxdev_sym3(P,Psig,calF,n)
% computes max_{f\in F} (1/n) sum_i sig_i(f(X_i)-f(Y_i))
% i.e., second symmetrization
% where f: X -> R
% each column of F is such an f

%f = [1:m]';
%Psig = stat_sym_sig(P,m,n,f);
%Psig = ones(2^n,1); Psig = Psig/sum(Psig);
[m,F] = size(calF);

E = 0;
for xi=1:m^n
  x = i2c(xi,m,n);
  FX = getFX(calF,x);
  for si=1:2^n
    sig = 2*(i2c(si,2,n)-1)-1;
    SIG = repmat(sig,[F 1]);
    Z = max(sum(SIG.*(FX),2)/n);
    E = E + Z * Psig(si) * P(xi);
  end
end

return

function FX = getFX(calF,x)
[m,F] = size(calF);
n = length(x);
FX = zeros(F,n);
for f=1:F
  for i=1:n
    FX(f,i) = calF(x(i),f);
  end
end
return


function c=i2c(i,m,n)
dims = repmat(m,[1 n]);
c = ind2coord(i,dims);
return